Results 121 to 130 of about 248 (141)

Functional Bregman divergence

2008 IEEE International Symposium on Information Theory, 2008
To characterize the differences between two positive functions or two distributions, a class of distortion functions has recently been defined termed the functional Bregman divergences. The class generalizes the standard Bregman divergence defined for vectors, and includes total squared difference and relative entropy.
Bela A. Frigyik, Santosh Srivastava, Maya R. Gupta   +2 more
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Quasiconvex Jensen Divergences and Quasiconvex Bregman Divergences

2021
We first introduce the class of strictly quasiconvex and strictly quasiconcave Jensen divergences which are asymmetric distances, and study some of their properties. We then define the strictly quasiconvex Bregman divergences as the limit case of scaled and skewed quasiconvex Jensen divergences, and report a simple closed-form formula which shows that ...
Frank Nielsen, Gaëtan Hadjeres
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Bregman Divergences from Comparative Convexity

2017
Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We define and study the Bregman divergences with respect to comparative convexity. As an example, we consider the convexity induced by quasi-arithmetic means, report explicit formulas, and show that those Bregman divergences are ...
Frank Nielsen, Richard Nock
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Bregman Divergences and Multi-dimensional Scaling

2009
We discuss Bregman divergences and the very close relationship between a class of these divergences and the regular family of exponential distributions before applying them to various topology preserving dimension reducing algorithms. We apply these to multidimensional scaling (MDS) and show the effect of different Bregman divergences. In particular we
Pei Ling Lai, Colin Fyfe
openaire   +1 more source

Information Geometry of U-Boost and Bregman Divergence

Neural Computation, 2004
We aim at an extension of AdaBoost to U-Boost, in the paradigm to build a stronger classification machine from a set of weak learning machines. A geometric understanding of the Bregman divergence defined by a generic convex function U leads to the U-Boost method in the framework of information geometry extended to the space of the finite measures over
Noboru Murata, Takashi Takenouchi, Takafumi Kanamori, Shinto Eguchi   +3 more
openaire   +3 more sources

Extending Metric Multidimensional Scaling with Bregman Divergences

Pattern Recognition, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jigang Sun, Malcolm K. Crowe, Colin Fyfe
openaire   +2 more sources

Bayes Risk Error is a Bregman Divergence

IEEE Transactions on Signal Processing, 2011
In previous work reported in these Transactions, we proposed a new distortion measure for the quantization of prior probabilities that are used in the threshold of likelihood ratio test detection: Bayes risk error. In this correspondence, we show that the Bayes risk error is a member of the class of Bregman divergences and discuss the implications of ...
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Bregman Divergences and the Self Organising Map

2008
We discuss Bregman divergences and the very close relationship between a class of these divergences and the regular family of exponential distributions before applying them to various topology preserving dimension reducing algorithms. We apply these methods to identification of structure in magnetic resonance images of the brain and show that different
Eunsong Jang, Colin Fyfe, Hanseok Ko
openaire   +1 more source

Generalized Fisher Kernel with Bregman Divergence

2022
Pau Figuera, Alfredo Cuzzocrea, Pablo García Bringas   +2 more
openaire   +2 more sources

Coresets and Approximate Clustering for Bregman Divergences

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, 2009
Marcel R. Ackermann, Johannes Blömer
openaire   +1 more source